Problem: Factor completely. $9m^2+30mn+25n^2=$
Solution: $\begin{aligned} &\phantom{=}9m^2+30mn+25n^2 \\\\ &= ({3m})^2+2({3m})({5n})+({5n})^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({3m})^2+2({3m})({5n})+({5n})^2 \\\\ &=({3m}+{5n})^2 \end{aligned}$ In conclusion, $9m^2+30mn+25n^2=(3m+5n)^2$ Remember that you can always check your factorization by expanding it.